What does it mean for a neuron in a neural network to be activated?
A neuron is said activated when its output is more than a threshold, generally 0.

For examples :
\begin{equation}
y = Relu(a) &gt; 0
\end{equation}
when 
\begin{equation}
a = w^Tx+b &gt; 0
\end{equation}

Same goes for sigmoid or other activation functions.